4. Common support#

Common support requires overlap across treatment groups. The ModifiedCausalForest checks estimated treatment probabilities before effect estimation and removes observations outside the selected support. This changes the population to which the results apply.

cs_type=0 disables the adjustment.
cs_type=1 (default) intersects treatment-group probability ranges.
cs_type=2 retains a row only when every treatment probability lies in [cs_min_p, 1 - cs_min_p]. Both endpoints are included.

Probability models use classification forests. With lc_cs_cv=True, construction predictions are cross-fitted; filling and prediction observations use the average of the fitted fold models. Alternatively, lc_cs_cv=False reserves a separate sample for fitting these models.

4.1. Advanced options#

For type 1, let \(L_{gj}\) and \(U_{gj}\) be the \((1-q)\) and \(q\) quantiles of probability \(p_j(X)\) within observed treatment group \(g\), where cs_quantil=q. For \(q=1\), use the group minima and maxima. With cs_adjust_limits=a, the bounds are

\[\begin{split}\mathrm{lower}_j &= \max_g \operatorname{clip}((1-a)L_{gj},0,1), \\ \mathrm{upper}_j &= \min_g \operatorname{clip}((1+a)U_{gj},0,1).\end{split}\]

For example, cs_quantil=0.95 uses the 5th and 95th percentiles of each estimated treatment probability, calculated separately within each observed treatment group. These bounds are widened using cs_adjust_limits. The common-support interval then runs from the largest lower bound to the smallest upper bound across treatment groups.

With cs_type=1, this check uses the estimated probabilities of all treatments except the first. With cs_type=2, every estimated treatment probability must lie between cs_min_p and 1 - cs_min_p, including the endpoints.

cs_max_del_train sets the maximum proportion of observations that may be removed by the common-support adjustment in the training data. This limit is checked separately for the sample used to construct the trees and the sample used to fill their leaves with outcomes.

For example, a value of 0.5 stops estimation if more than 50% of either sample is removed. In that case, inspect the data and the overlap between treatment groups before changing the common-support settings.

This limit does not apply to prediction data. Prediction observations outside the estimated common support are still removed, but their removal share is not restricted by cs_max_del_train.

4.2. Parameter overview#

Parameter	Purpose
`cs_type`	No adjustment (0), intersected group ranges (1), or fixed bounds (2).
`cs_min_p`	Lower bound for type 2; the upper bound is one minus this value. Default: 0.01.
`cs_quantil`	Type-1 quantile setting. Default: 1 (minima/maxima).
`cs_adjust_limits`	Relaxes type-1 ranges before intersection.
`cs_max_del_train`	Maximum training deletion share, checked in each sample. Default: 0.5.

4.3. Inspecting retained observations#

The following fragment uses an initialized my_mcf and prepared training and prediction data. It learns support rules without building a forest:

my_mcf.train(training_df, exit_after_commonsupport=True)
support = my_mcf.predict(prediction_df, exit_after_commonsupport=True)
retained_df = support['inputdata_on_support']

inputdata_on_support contains the observations remaining after data preparation and the common-support adjustment. When output is enabled, the returned probability tables include an on_support column indicating which observations passed the common-support check. Observations removed during earlier data preparation are not included in these tables.

When you also estimate treatment effects, iate_data_df contains the remaining prediction observations together with their estimated effects and potential outcomes. This dataframe is available only when IATE estimation and dataframe output are enabled.

See train() and predict() for the returned table names.

4.4. Examples#

from mcf.example_data import example_data
from mcf.mcf_main import ModifiedCausalForest

# Generate example data using the built-in function `example_data()`
training_df, prediction_df, name_dict = example_data()


my_mcf = ModifiedCausalForest(
        var_y_name="outcome",
        var_d_name="treat",
        var_x_name_ord=["x_cont0", "x_cont1"],
        # Turn common support adjustments off:
        cs_type=0)


my_mcf = ModifiedCausalForest(
    var_y_name="outcome",
    var_d_name="treat",
    var_x_name_ord=["x_cont0", "x_cont1", "x_ord1"],
    # Use automatic common support adjustments
    cs_type=1,
    # Offset the cut-off limits: Multiply the upper cut-off by 1.1 and the
    # lower cut-off by 0.9:
    cs_adjust_limits=0.1,
    # Raise an exception if more than 25% of the observations are dropped:
    cs_max_del_train=0.25)


my_mcf = ModifiedCausalForest(
    var_y_name="outcome",
    var_d_name="treat",
    var_x_name_ord=["x_cont0", "x_cont1", "x_ord1"],
    # Use common support adjustments and specify cut-off probabilities manually:
    cs_type=2,
    cs_min_p=0.05)